3. Unsteady Fountain (30 pts) The figure below shows an unsteady fountain. The water exits the 2 cm diameter nozzle in the vertical direction with a sinusoidal velocity variation in time: V(t) = 20 (2+ sin (wt)) The frequency, w = =2f, will be varied in this fountain, allowing the pulsing of the fountain to vary from slow (f = 0.2 Hz) to fast (f = 2 Hz). You will be asked to find the flange force required to hold the fountain in place for these different conditions. Be sure to fully list and justify any assumptions you make. Dia = 5cm V(t) 20[2+ sin(wt)] m/s Dia = 2cm 10cm 5m Figure 2: Diagram of the pulsing fountain a) Determine the total mass of water ejected from the fountain per full pulsing cycle when the pulse rate is (i) 0.2 Hz and (ii) 2 Hz b) Determine and plot the flange force in the x- and the y-directions as a function of time for (i) 0.2 Hz and (ii) 2 Hz c) Determine and plot the flange moment (i.e. torque) as a function of time for (i) 0.2 Hz and (ii) 2 Hz